Environmental Engineering Reference
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where
d
V
T
= wind speed deficit caused by the tower (m/s)
W
T
=
tower shadow shape function
t
0
, t
p
= empirical scale constants
y
0
=
half-angle of tower shadow sector (rad)
k
=
number of waves in the tangential profile of the shadow
The parameters
t
0
,
t
p
,
y
0
, and
k
are selected to give the desired approximation for the
tangential profile of wind speed in a pie-shaped region with a central angle of 2y
0
, centered
on a blade azimuth angle of p
.
For example, the shadow of a shell tower is often modeled
as a sin
2
function using the following parameter values:
t
0
= t
p
=
one-half the maximum ratio of deficit to free-stream wind speed
k =
1
A truss tower with three legs produces a shadow with three peaks, and this is modeled by
selecting
k
= 3.
Spatial Turbulence Model
As discussed in Chapter 8 and illustrated in Figures 8-16 and 8-29, small-scale
turbulence (
i.e.
having significant spatial variations in wind speed within the swept area of
the rotor) will cause a moving rotor blade to experience a wind power spectrum with peaks
at multiples of the rotor speed. In effect, the blade will be subject to harmonic forcing
functions with frequencies at integer multiples of its rotational speed, and it will respond
dynamically to them. Estimating the amplitudes of these turbulence forcing functions is
beyond the scope of this chapter and is, in fact, the subject of continuing research on wind
characteristics. For example, see Equations (2-28) to (2-35) [Spera 1995]. Here we will make
provision for wind turbulence excitations and emphasize that the harmonic content of these
excitations plays an important role in determining the structural-dynamic response of wind
turbine blades.
We shall assume that the distribution of turbulence-induced variations in wind speed
across the rotor swept area changes slowly compared to the period of rotor rotation, so our
model will be non-uniform in space but uniform in time. In the general case illustrated in
Figure 11-1, the wind turbulence will have components in all three of the
X-Y-Z
directions,
and each of these may vary with position in the rotor disk area. Thus
é
ê
ë
d
u
(
r
, y, 0)
d
v
(
r
, y, 0)
d
w
(
r
, y, 0)
d
U
(
r
, y,
t
) =
(11-12)
where
d
U
(
r
,y,
t
) = turbulence in the free-stream horizontal wind (m/s)
d
u
(
r
,y,0)
=
spatial turbulence in the
X
direction (m/s)
d
v
(
r
,y,0) = spatial turbulence in the
Y
direction (m/s)
d
w
(
r
,y,0) = spatial turbulence in the
Z
direction (m/s)
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